It is worth noting that closed-loop stability of the function approximation methods above, except [1]}, requires reasonable convergence of NN model to the original control law.
Nevertheless, training a NN is commonly a high-dimensional nonlinear program.
This nonlinear program is solved with faith by a black-box solver, such as [2]}, which in general does not come with any guarantee on convergence or optimality.
Hence, for most of the existing works, their closed-loop stability replies in large part on the faithful assumption that there exists a black-box optimization procedure that can somehow find a good approximation to the original MPC.
